Appearance-Based Classification and Recognition Using Spectral Histogram Representations and Hierarchical Learning for OCA

This thesis is composed of two parts. Part one is on Appearance-Based Classification and Recognition Using Spectral Histogram Representations. We present a unified method for appearance-based applications including texture classification, 2D object recognition, and 3D object recognition using spectral histogram representations. Based on a generative process, the representation is derived by partitioning the frequency domain into small disjoint regions and assuming independence among the regions.This give rise to a set of filters and a representation consisting of marginal distribution of those filers responses. We provide generic evidence for its effectiveness in characterizing object appearance through statistical sampling and in classification by visualizing images in the spectral histogram space. We use a multilayer perception as the classifier and propose a selection algorithm by maximizing the performance over training samples. A distinct advantage of the representation is that it can be effectiveness used for different classification and recognition tasks. The claim is supported by experiments and comparisons in texture classification, face recognition, and appearance-based 3D object recognition. The marked improvement over existing methods justifies the effectiveness of the generative process and the derived spectral histogram representation. Part two is on Hierarchical Learning for Optimal Component Analysis. Optimization problems on manifolds such as Grassmann and Stiefel have been a subject of active research recently. However the learning process can be slow when the dimension of data is large. As a learning example on the Grassmann manifold, optimal component analysis (OCA) provides a general subspace formulation and a stochastic optimization algorithm is used to learn optimal bases. In this paper, we propose a technique called hierarchical learning that can reduce the learning time of OCA dramatically. Hierarchical learning decomposes the original optimization problem into several levels according to a specially designed hierarchical organization and the dimension of the data is reduced at each level using a shrinkage matrix. The learning process starts from the lowest level with an arbitrary initial point. The following approach is then applied recursively: (i) optimize the recognition performance in the reduced space using the expanded optimal basis learned from the next lower level as an initial condition, and (ii) expand the optimal subspace to the bigger space in a pre-specified way. By applying this decomposition procedure recursively, a hierarchy of layers is formed. We show that the optimal performance obtained in the reduced space is maintained after the expansion. Therefore, the learning process of each level starts with a good initial point obtained from the next lower level. This speeds up the original algorithm significantly since the learning is performed mainly in reduced spaces and the computational complexity is reduced greatly at each iteration. The effectiveness of the hierarchical learning is illustrated on two popular data-sets, where the computation time is reduced by a factor of about 30 compared to the original algorithm.